Question

AD is the bisector of $\angle A$ of $\Delta ABC,AC=4.2cm,DC=6cm,BC=10cm$, then AB is:

• A. $2.8cm$
• B. $3cm$
• C. $3.5cm$
• D. none of these

Answer 1

The correct option is A $2.8cm$

Given $△ABC$, $AD$ is the bisector of angle $A$

And $AC=4.2$ cm ,$DC=6$ cm and $BC=10$ cm

Then $BD=10-6=4$ cm

we know that by internal angle bisector theorem, the bisector of a vertical angle of a triangle divides the base in the ratio of the other two sides

$\therefore \frac{AB}{AC}=\frac{BD}{DC}$

$\Rightarrow \frac{AB}{4.2}=\frac{4}{6}$

$\Rightarrow AB=\frac{4.2\times 4}{6}=2.8cm$